And coming to problem adjacent faces of number 4 are 1,2,5,6(remember that number 1 is at bottom).

So number 4 is opposite to number 3.

Now consider fourth dice,we have the following numbers on the
forward face=2
right face=4
left face=3 (since 4 is opposite to 3)
bottom face=1 (which we got earlier from given condition)

Now we left with top and backward faces.
From given data even numbered dices have only even number on their top faces. So,we left only with one even number 6.

Therefore
top face=6
backward face=5. and 1 is opposite to 6

Second,fourth,sixth dices have 1 on bottom face.so they all have number 6 on their top.

Hence total number of dots on thier top faces is 6+6+6 = 18.

Venky said:
(Wed, Aug 24, 2011 06:42:02 PM)

Anand kumar your great.

Sameeksha said:
(Sun, Aug 28, 2011 04:04:15 PM)

Yup great explanation anand:).

Nisha said:
(Mon, Sep 5, 2011 10:49:22 AM)

Well done Anand. :-)

Vadivelu said:
(Tue, Sep 6, 2011 05:20:19 PM)

-

Rohit Dakave said:
(Sat, Jan 7, 2012 11:21:06 AM)

Consider a dice,opposite faces are always in pairs(1,6)(2,5)(3,4)

->"No need to look at the condition"

1)In 1st ques we want even numbered dice i.e 2,4 and 6th dice top faces with even no.
from fig(2) we can see that 4 and 5 are visible means we have 3 opposite of 4 and 2 opposite of 5.so now we are left with 1 and 6.
now we want 6 at the top(even)so 1 wiil be at the bottom face
so from 2nd dice we got 6

Similarly in 4th dice we can see 2 and 4, means 5 will be opposite of 2 and 3 will opposite of 4 left with 1 and 6
we want 6(even) at the top so 1 wiil be at the bottom face
so from 4th dice we get 6

Similarly in 6th dice we can see 4 and 5, means 3 will be opposite of 4 and 2 will opposite of 5 left with 1 and 6
we want 6(even) at the top so 1 wiil be at the bottom face
so from 6th dice we get 6

Adding 6+6+6=18.

Using above procedure rest of the problems can be solved easily.

Angel said:
(Sun, Mar 18, 2012 12:00:56 AM)

Rohit best explanation! keep it up !

Sujith(Spt) said:
(Wed, Apr 17, 2013 10:41:19 AM)

Keep in mind that the sum of the numbers of dots on the opposite face is 7.
take 4 dotted face : here from figure the adjacent faces are [5,3,2] and the remaining are {1,3} so opp. to 4 is 3 (4+3=7).

Take 5 dotted face : here from figure the adjacent faces are [4,1] and the remaining are {2,3,6} so opp. to 5 is 2 (5+2=7).

Take 6 dotted face : here from figure the adjacent faces are [3,5] and the remaining are {1,2,4} so opp. to 6 is 1 (6+1=7).

Keep in mind that here even numbers can only be 2,4,and 6.

Now consider (II) : here 4 is there,and opp. to 5 is 2 then only possibility is 6 on top.

Consider (IV): here 2 and 4 is there then only possibility is 6 on top.
Consider (VI): same as (II). so 6 on top.

So adding 6+6+6 = 18 is the answer.

Rahul said:
(Tue, May 13, 2014 01:01:29 AM)

Nicely explained but too long answer I don't think this will come for nata exam.

Arun said:
(Tue, Nov 4, 2014 12:00:44 PM)

I think 2 4 6 dice contain 9, 6, 9 dots so answer will be 24 I think once 0 through this.